I am writing a guide on how to best farm for weapons to help level up your own weapons. This will be slightly incomplete due to not wanting to start a new game right away to find when weapon upgrading is possible at the soonest per character. But I will try to at least point out places to visit pre-Postgame (eventually).
The first thing about weapon farming is when you start off doing it you will be relying on Noelle. Noelle's Let's Trade attack let's you steal a monster's rare item, and there are many mobs throughout the game that have weapons as their rares. Noelle also has her Gimme a Present! limit break which steals ALL the monster's bling bling in one shot. When using her limit break and Gimme isn't listed at the top, always choose the bottom option in order to maximize the chance of her gaining another limit attack and thus another chance at getting the Gimme break.
Using Noelle this way can help get weapons but can be tedious since you can't always get her ultimate limit, but can help when moving on to the next step.
This next step is mostly for post game weapon farming but is feasible to do while going through story mode.
I got bored trying to have Noelle be my thief so I decided t make 'thief weapons' for all my characters. I call them thief weapons because every weapon has the Steal ability on them.
Here is one of my 'thief weapons', the other's will be shown in my following posts.
Noelle's
With the steal ability on a weapon it gives every attack, not hit, the ability to steal either the rare or the ultra rare item from a mob. Again, the steal ability only applies to each attack, not to each hit. So even if Litany uses her Ablution limit ability, although it hits for 50+ times, she will still only get the one chance at stealing, not 50+ attempts.
Note that even with 100 in that stat, it does not guarantee a steal even if the enemy has not be stolen from yet. I do not know the mathematics behind the Steal stat but 100 does not equal success, so I think that Steal is either capped at a lower percant than the stat shows, or perhaps the higher the stat number is the more likely you are at stealing the ultra rare, or maybe at 100 you attempt to steal every time (which seems to be the case).
Getting Brake onto your thief weapon is invaluable, especially for Noelle at the start.
The three female characters all get All Enemy attacks, Izayoi gets column and a row attack. With Steal and Brake on a weapon you have an increased chance of a limit break happening, which is amazeballs when on a female weapon. This will increase the likelyhood of stealing from EVERY single mob, so long as the limits that show up include an All Enemy attack. This equates to more stealing chances per enemy, per battle.
I do not know when you can start encountering the steal stat, perhaps from the very beginning. If someone could verify if you can start seeing it at the beginning or if it starts only at a certain point I can put that into this little mini-guide which would be useful for when you can start effectively stealing without having to rely on a limit break.
EDIT
Also it is worth noting that stealing an item does not remove that item from an enemy to drop from being defeated. So yes, it is possible to get two Dainsleifs from one Chaos Dragon. So pretty much you turn into Oprah by being able to say "YOU get a weapon, and YOU get a weapon, EVERYBODY gets a weapon!!"